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4540mida_w11.pdf

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Department
Administrative Studies
Course Code
ADMS 4540
Professor
William Lim

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AP/ADMS 4540 Financial Management
Winter 2011
Mid-term Exam Answer Key Instructor: Dr. William Lim
Question 1 (8 marks)
Calculate the duration and volatility of a 5-year, $1,000 face value, 14 percent coupon bond yielding 15 percent
with coupons paid annually. Using its duration and volatility, calculate what happens to the price of the bond
when the yield to maturity falls to 14 percent. What are the consequences for a financial institution that does not
match the duration of its assets to the duration of its liabilities?
Time Payment PV RV WV
1 140 121.74 0.12596 0.12596
2 140 105.86 0.10953 0.21906
3 140 92.05 0.09524 0.28572
4 140 80.04 0.08282 0.33128
5 1,140 566.78 0.58645 2.93225
Bond Price = 966.47 1.00000 3.89427=Duration
Duration = D = 3.89427 years [4 marks for table and D]
Volatility = v = -D/(1+r) = -3.89427/1.15 = -3.416% [1 mark for v]
When yield falls by one percent, price rises by 3.416% or $33.01
New price = $966.47+$33.01 = $999.48. [1 mark for new price]
Without duration matching, say with duration of assets much longer than duration of liabilities, a financial
institution's net worth (assets less liabilities) will suffer when interest rates rise. The value of longer
duration assets will fall much more than the value of shorter duration liabilities, with a resulting loss of net
worth and possible insolvency. [2 marks]
Question 2 (15 marks)
With Canadian interest rates still at historical lows, McGraw-Hill-Ryerson (MHR) is considering whether to
take advantage of its lower cost of debt and refund its old bonds. Suppose the old issue comprises $30 million,
12 percent coupon rate (paid yearly) 20-year bonds that were sold 5 years ago. A new issue of $30 million, 15-
year bonds can be sold with a coupon rate of 9 percent (paid yearly). A call premium of 6 percent will be
required to retire the old bonds and floatation costs of $1 million will apply to the new issue. The marginal tax
rate applicable is 50% and it is expected that there will be a one month overlap during which any funds can be
invested in Treasury bills yielding 8 percent. Should MHR refund?
2
Question 3 (15 marks)
Three BAS students and you are interviewing in a roundtable for employment in a prestigious asset
management firm run by George and The Man. The interviewer decides to test potential employees by
presenting them with the following question: “Consider two mutually exclusive projects with net costs and
benefits measured by the following cash flows:
Year Project A Project B
2004 -$1,000 -$1,000
2005 0 +$460
2006 0 +$460
2007 0 +$460
2008 0 0
2009 +$1,925 0
Which project should a firm undertake?
The three BAS students gave different answers.
Larry: “It’s obvious that a firm should undertake Project A because it offers $545 more in net benefits than
does Project B.”
Curley: “I think a firm should undertake Project B because it has a higher internal rate of return: approximately
19 percent as opposed to approximately 15 percent.”
Moe: “Actually, there is really little difference between the projects. Take any discount rate, say 11.6 percent.
The NPV of each project is about $112. It doesn’t matter which one we choose.”
You are the fourth and final student to speak.
3a. Draw a diagram of the net present value profiles of both projects. (4 marks)
3b. Provide a valid critique of Larry, Curley and Moe’s answers. (8 marks)
3c. Provide a brief description of the correct method by which the projects should be evaluated. (3 marks)
3a. (4 marks)
3b. Larry does not take into account the time value of money. (The opportunity cost of capital is almost
never zero.) Curley needs to realize the deficiencies of the IRR and the superiority of NPV over IRR. The first
deficiency of IRR is that it does not ask, if the project is done, how much will the firm’s value increase or
decrease. Could a shareholder maintain the planned pattern of consumption and add something to it? Second,
the NPV reflects the absolute size of the project while the IRR does not. The IRR is biased against larger
projects. Third, the NPV uses the opportunity cost of capital as the reinvestment rate while the IRR reinvests at
the project’s own IRR. Thus IRR is biased against projects with returns farther into the future and may lead to
myopic decision making. Fourth, NPV also has important technical advantages. For example, when
nonconventional cash flows are considered, a solution for the project’s IRR may not exist; in other instances,
more than one IRR may be found for a single project. Fifth, NPV answers the question, would this project
increase consumption for the investor. Moe has figured out the cross-over point (Fisher IRR), but needs to take
into account the opportunity cost of capital to make the cross-over point relevant for decision making. (8 marks)
3c. First, find the opportunity cost of capital to determine the required return. Then use it to calculate the NPV
of cash flows of projects A and B. (3 marks)
NPV Profiles
-400
-200
0
200
400
600
800
1000
0 5 10 15 20
r
NPV
NPV(A)
NPV(B)

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Description
AP/ADMS 4540 Financial Management Winter 2011 Mid-term Exam Answer Key Instructor: Dr. William Lim Question 1 (8 marks) Calculate the duration and volatility of a 5-year, $1,000 face value, 14 percent coupon bond yielding 15 percent with coupons paid annually. Using its duration and volatility, calculate what happens to the price of the bond when the yield to maturity falls to 14 percent. What are the consequences for a financial institution that does not match the duration of its assets to the duration of its liabilities? Time Payment PV RV WV 1 140 121.74 0.12596 0.12596 2 140 105.86 0.10953 0.21906 3 140 92.05 0.09524 0.28572 4 140 80.04 0.08282 0.33128 5 1,140 566.78 0.58645 2.93225 Bond Price = 966.47 1.00000 3.89427=Duration Duration = D = 3.89427 years [4 marks for tableand D] Volatility = v = -D/(1+r) = -3.89427/1.15 = -3.416% [1 mark for v] When yield falls by one percent, price rises by 3.416% or $33.01 New price = $966.47+$33.01 = $999.48. [1 mark for new price] Without duration matching, say with duration of assets much longer than duration of liabilities, a financial institution’s net worth (assets less liabilities) will suffer when interest rates rise. The value of longer duration assets will fall much more than the value of shorter duration liabilities, with a resulting loss of net worth and possible insolvency. [2 marks] Question 2 (15 marks) With Canadian interest rates still at historical lows, McGraw-Hill-Ryerson (MHR) is considering whether to take advantage of its lower cost of debt and refund its old bonds. Suppose the old issue comprises $30 million, 12 percent coupon rate (paid yearly) 20-year bonds that were sold 5 years ago. A new issue of $30 million, 15- year bonds can be sold with a coupon rate of 9 percent (paid yearly). A call premium of 6 percent will be required to retire the old bonds and floatation costs of $1 million will apply to the new issue. The marginal tax rate applicable is 50% and it is expected that there will be a one month overlap during which any funds can be invested in Treasury bills yielding 8 percent. Should MHR refund? Question 3 (15 marks) Three BAS students and you are interviewing in a roundtable for employment in a prestigious asset management firm run by George and The Man. The interviewer decides to test potential employees by presenting them with the following question: “Consider two mutually exclusive projects with net costs and benefits measured by the following cash flows: Year Project A Project B 2004 -$1,000 -$1,000 2005 0 +$460 2006 0 +$460 2007 0 +$460 2008 0 0 2009 +$1,925 0 Which project should a firm undertake?” The three BAS students gave different answers. Larry: “It’s obvious that a firm should undertake Project A because it offers $545 more in net benefits than does Project B.” Curley: “I think a firm should undertake Project B because it has a higher internal rate of return: approximately 19 percent as opposed to approximately 15 percent.” Moe: “Actually, there is really little difference between the projects. Take any discount rate, say 11.6 percent. The NPV of each project is about $112. It doesn’t matter which one we choose.” You are the fourth and final student to speak. 3a. Draw a diagram of the net present value profiles of both projects. (4 marks) 3b. Provide a valid critique of Larry, Curley and Moe’s answers. (8 marks) 3c. Provide a brief description of the correct method by which the projects should be evaluated. (3 marks) 3a. (4 marks) NPV Profiles 1000 800 600 400 NPV(A) NP200 NPV(B) 0 -2000 5 10 15 20 -400 r 3b. Larry does not take into account the time value of money. (The opportunity cost of capital is almost never zero.) Curley needs to realize the deficiencies of the IRR and the superiority of NPV over IRR. The first deficiency of IRR is that it does not ask, if the project is done, how much will the firm’s value increase or decrease. Could a shareholder maintain the planned pattern of consumption and add something to it? Second, the NPV reflects the absolute size of the project while the IRR does not. The IRR is biased against larger projects. Third, the NPV uses the opportunity cost of capital as the reinvestment rate while the IRR reinvests at the project’s own IRR. Thus IRR is biased against projects with returns farther into the future and may lead to myopic decision making. Fourth, NPV also has important technical advantages. For example, when nonconventional cash flows are considered, a solution for the project’s IRR may not exist; in other instances, more than one IRR may be found for a single project. Fifth, NPV answers the question, would this project increase consumption for the investor. Moe has figured out the cross-over point (Fisher IRR), but needs to take into account the opportunity cost of capital to make the cross-over point relevant for decision making. (8 marks) 3c. First, find the opportunity cost of capital to determine the required return. Then use it to calculate the NPV of cash flows of projects A and B. (3 marks) Question 4 (32 marks) After the interview, you meet (Curious) George and The Man (with the Yellow Hat). They are financial managers who network with other managers and analysts. Hoping to work in the industry, you follow them around to impress them and their friends with your knowledge of finance. 4a. You next meet Professor Wiseman. She provides you with the following table which gives some characteristics of two risky assets - stocks and bonds. Also shown are weights in the market portfolio P, which is assumed to be mean-variance efficient, i.e., it provides the highest expected return for its level of variance. Asset Weigh in Market Expected Standard Correlation Correlation Portfolio P Return Deviation With Stocks With Bonds Stocks 0.50 ? 0.20 1.00 0.40 Bonds 0.50 ? 0.10 0.40 1.00 If the expected return on the market portfolio P, E(rP) is equal to 0.10 or 10 percent, what are the expected returns on stocks and bonds? Assume the risk-free rate,fr , is equal to 0.05 or 5 percent and show all calculations clearly. (8 marks) 4b. George and The Man visit Caill
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